Polarization-independent waveguide-type optical interference circuit

ABSTRACT

A Mach-Zehnder interferometer circuit ( 700 ) is provided with two couplers ( 722, 724 ) and two arm waveguides ( 706, 708 ) connecting the couplers with each other, each fabricated on a substrate, in which a polarization rotation device ( 732 ) is disposed in a groove dividing each of the two arm waveguides into two, the polarization rotation device ( 732 ) for converting vertically polarized light into horizontally polarized light, and birefringence is adjusted by performing laser irradiation or the like partially into at least one of the two arm waveguides such that a difference between birefringence values divided by an optical wavelength to be used is within a range of 2 m-0.2 to 2 m+0.2 (m is an integer including zero), the birefringence values being those integrated linearly along the respective two arm waveguides in an optical signal travelling direction.

TECHNICAL FIELD

The present invention relates to a polarization-independentwaveguide-type optical interference circuit which suppressespolarization dependence and temperature dependence regardingpolarization.

BACKGROUND ART

A further demand of a longer distance and a larger capacitance inoptical communication has been making wavelength multiplex communicationan important technology. A device indispensable to this wavelengthmultiplex communication system includes a wavelengthmultiplexing/demultiplexing filter for multiplexing/demultiplexingwavelength of an optical signal. For example, a simple wavelengthmultiplexing/demultiplexing filter includes a Mach-Zehnderinterferometer circuit (hereinafter, called MZI) using an opticalwaveguide (refer to, e.g., Non-patent document 1).

FIG. 1 shows a schematic diagram of this MZI. An MZI 100 is providedwith two couplers (122 and 124) and arm waveguides (106, 108) connectingthe two couplers with each other, and the coupler 122 is provided withtwo input waveguides (102, 104) and the coupler 124 is provided with twooutput waveguides (110, 112).

Hereinafter, the operation principle and polarization dependence of theMach-Zehnder interferometer will be explained.

In the MZI 100, a path from an input 11 (input waveguide 102) to anoutput O1 (output waveguide 110) is defined as a through-path and a pathfrom an input 11 (input waveguide 102) to an output O2 (output waveguide112) is defined as a cross path. In this case, optical outputs(O^(through) and O^(cross)) of the respective paths are described asfollows by using the publicly known interference principle (here, acoupling ratio of the coupler is assumed to be 50%).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 1} \right\rbrack & \; \\{O^{through} = {I_{0}{\sin^{2}\left( {\frac{n\;\Delta\; L}{2} \cdot \frac{2\;\pi}{\lambda}} \right)}}} & (1) \\{O^{cross} = {I_{0}{\cos^{2}\left( {\frac{n\;\Delta\; L}{2} \cdot \frac{2\;\pi}{\lambda}} \right)}}} & (2)\end{matrix}$

Here, I₀ indicates the optical intensity of input light, n indicates aneffective refraction index, ΔL indicates a path difference between thetwo arm waveguides, and λ indicates a wavelength to be used.

The optical signal is extinguished and output to the other pathperiodically at signal wavelengths which satisfy nΔL=λm in Formula (1)for the through path and the following condition in Formula (2) for thecross path (m is integer), and the through-path and the cross pathfunction as a wavelength multiplexing/demultiplexing filter.

$\begin{matrix}{{n\;\Delta\; L} = {\lambda\left( {m + \frac{1}{2}} \right)}} & \left\lbrack {{Formula}\mspace{14mu} 2} \right\rbrack\end{matrix}$(m: integer)

The following is a fabrication method of the optical waveguide used forsuch a device.

A lower under-clad layer mainly made of SiO₂ and a core layer made ofSiO₂ doped with GeO₂ are deposited sequentially on a silicon substrateby the use of a flame deposition method. Subsequently, the core layer ispatterned by the use of reactive ion etching. Then, by another use ofthe flame deposition method, an over-clad layer is deposited tofabricate an embedded optical waveguide.

Usually, such an optical waveguide has birefringence because of stresscaused by a core shape or a difference between the thermal expansioncoefficients of the substrate and the clad. That is, the effectiverefraction indexes (n_(TE) and n_(TM)) are different from each otherbetween a TM polarized wave which has a polarization directionperpendicular to the substrate and a TE polarized wave which has apolarization direction parallel to the substrate. Here, an optical pathlength difference depending on the polarization Δ(BL) is given by thefollowing formula.[Formula 3]Δ(BL)=∫Bdl ₁ −∫Bdl ₂  (3)

Here, l₁ and l₂ are coordinates along the two arm waveguides,respectively.

Further,∫Bdl ₁ and ∫Bdl ₂  [Formula 4]are the birefringence values integrated linearly along the armwaveguides, respectively.

Since the optical path length difference depending on the polarizationΔ(BL) has a finite value, a polarization dependence is caused in theextinction wavelength. This polarization dependence causes theoccurrence of polarization dependent loss (PDL) and polarizationdependent frequency difference (PDf) and deteriorates signal qualityconsiderably.

The following is known as methods for eliminating this polarizationdependence.

(First Example of a Conventional Technique)

There is disclosed a Mach-Zehnder interferometer circuit in which ahalf-wave length plate corresponding to one half of the wavelength to beused is inserted on a straight line connecting the centers of the twoarm waveguides with each other so as to have the principal axis thereofinclined at an angle of 45 degrees relative to the horizontal direction(or vertical line) of the substrate plane (refer to Non-patent document2).

FIG. 2 shows a schematic diagram of the MZI in the first example of theconventional technique. An MZI 200 is provided with two couplers (222,224) and two arm waveguides (206, 208) connecting the two couplers witheach other. Further, the MZI 200 is provided with a half-wave lengthplate 232 disposed so as to divide each of the arm waveguides (206, 208)into two. In addition, the coupler 222 is provided with two inputwaveguides (202, 204) and the coupler 224 is provided with two outputwaveguides (210, 212).

In the MZI 200, an optical signal travels half the distance of the armwaveguide (206, 208) up to the half-wave length plate 232 in the TEpolarization (or TM polarization) and is converted from the TEpolarization to the TM polarization (or from the TM polarization to theTE polarization) in the half-wave length plate 232. Then, the opticalsignal travels the remaining half distance of the arm waveguide (206,208) in the TM polarization (or TE polarization). The optical signalseach converted from the TE polarization (or TM polarization) into the TMpolarization (or TE polarization) have the optical path lengthdifference from each other shown by the following formula, and it ispossible to eliminate the optical path length difference depending onthe polarization Δ(BL).

$\begin{matrix}{{n\;\Delta\; L} = {\left( {n_{TE} + n_{TM}} \right) \cdot \frac{\Delta\; L}{2}}} & \left\lbrack {{Formula}\mspace{14mu} 5} \right\rbrack\end{matrix}$

(Second Example of a Conventional Technique)

There is known a Mach-Zehnder interferometer circuit which sets theoptical path length difference depending on the polarization Δ(BL) to bean integral multiple (including zero) of the optical wavelength to beused (refer to Patent document 1). This circuit sets the optical pathlength difference depending on the polarization Δ(BL) to be an integralmultiple (including zero) of the wavelength to be used focusing on thefact that the interference condition of the TM polarization coincideswith the interference condition of the TE polarization since theMach-Zehnder interferometer cannot discriminate the phase difference ofan integral multiple of the wavelength λ to be used.

However, the above described Mach-Zehnder interferometer circuits(hereinafter referred to as MZI) have the following problems.

The first example of the conventional technique is based on theassumption that the perfect polarization conversion is performed fromthe TE polarization into the TM polarization (or from the TMpolarization into the TE polarization) by using the half-wave lengthplate. However, the film thickness of the half-wave length plate isshifted from a desired thickness because of fabrication error and doesnot coincide with the design wavelength. As a result, the polarizationconversion is not performed perfectly from the TE polarization into theTM polarization and a part thereof remains as the TE polarization. Whensuch a half-wave length plate is used, the optical path lengthdifference of the TE polarized wave, which is input in the TEpolarization and travels without performing the polarization conversion,becomes n_(TE)ΔL, in the first example of the conventional technique.That is, the purpose of setting the optical path length difference to bethe value shown by the following formula without depending on thepolarization is not achieved and the polarization dependence occurs.

$\begin{matrix}{\left( {n_{TE} + n_{TM}} \right) \cdot \frac{\Delta\; L}{2}} & \left\lbrack {{Formula}\mspace{14mu} 6} \right\rbrack\end{matrix}$

For example, when the frequency space (period) of the extinctionwavelengths is defined as a FSR (Frequency Spectral Range) and themaximum value of the extinction wavelength difference depending on thepolarization is defined as a PDf (Polarization Dependent Frequency), thePDf becomes as large as 0.4 GHz for both of the cross path and thethrough-path in the Mach-Zehnder interferometer circuit which is thefirst example of the conventional technique and has a FSR of 10 GHz.This PDf is required to be one hundredth or less of the FSR for thepurpose of avoiding the degradation of the signal quality, and it isdifficult to satisfy the specification by the conventional technique.

The second example of the conventional technique has a problem that thePDf has a large birefringence dependence. As a result, it is verydifficult to satisfy the requirement that the PDf is one hundredth ofthe FSR and the temperature dependence also has a large PDf variation.This birefringence dependence will be briefly explained below.

The extinction frequencies of the TE polarized wave and the TM polarizedwave for the through-path are defined as follows, respectively.f _(TE) ^(th); and :f _(TM) ^(th)  [Formula 7]

The extinction frequencies satisfy the following formulas, respectively.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 8} \right\rbrack & \; \\{f_{TE}^{th} = {{mFSR}_{TE} = \frac{mc}{n_{TE}\Delta\; L}}} & (4) \\{f_{TM}^{th} = {{mFSR}_{TM} = \frac{mc}{n_{TM}\Delta\; L}}} & (5)\end{matrix}$

Here, m indicates an order number, FSR_(TE) and FSR_(TM) indicate theFSRs of the TE polarized light and the TM polarized light, respectively,and c indicates the light speed. By the use of the above two formulas,the PDf is converted into the following formula.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 9} \right\rbrack & \; \\\begin{matrix}{{PDf} = {\frac{f_{avg}^{th}}{n_{avg}}B}} & \left( {0 \leq B \leq {\frac{1}{2}\frac{\lambda}{\Delta\; L}}} \right)\end{matrix} & (6)\end{matrix}$

Here,

$\begin{matrix}{{f_{avg}^{th} = \frac{f_{TE}^{th} + f_{TM}^{th}}{2}},{n_{avg} = \frac{n_{TE} + n_{TM}}{2}},{B = {n_{TE} - n_{TM}}}} & \left\lbrack {{Formula}\mspace{14mu} 10} \right\rbrack\end{matrix}$

When the effective refraction index is 1.45 and the extinction frequencyis 193 THz, the above formula provides a PDf variation of 133×10¹²relative to the birefringence. This means the PDf has a variation aslarge as 1.33 GHz when the birefringence varies by 0.1×10⁻⁴, and it isfound that the PDf has a large birefringence dependence. Accordingly,the birefringence needs to be adjusted highly accurately and it is verydifficult to satisfy the condition that the PDf value is to be onehundredth of the FSR.

Meanwhile, internal stress applied to the waveguide is changed byenvironmental temperature because of thermal expansion coefficientdifference between the substrate and the clad or thermal expansioncoefficient difference between a board attaching the circuit and thecircuit. As a result, the birefringence value is changed through thephoto-elasticity effect and thereby the PDf is changed by theenvironmental temperature.

For example, in the Mach-Zehnder interferometer having a FSR of 10 GHzin which the birefringence is adjusted so as to reduce the PDf down to0.33 GHz by using the second example of the conventional technique,there arises a problem that the PDf varies as large as 6 GHz when theenvironmental temperature is changed from −10° C. to 80° C.

The present invention has been achieved in view of such a problem, andan object thereof is to provide a polarization-independentwaveguide-type optical interference circuit which suppresses thepolarization dependence of a transmission spectrum and the temperaturedependence regarding the polarization.

-   Patent document 1: Japanese Patent Laid-Open No. H06-60982 (1994)-   Patent document 2: Japanese Patent Publication No. 3703013-   Patent document 3: WO 01/059495-   Non-patent document 1: K. Inoue et al., “A Four-Channel Optical    Waveguide Multi/Demultiplexer for 5-GHz Spaced Optical FDM    Transmission”, JOURNAL OF LIGHTWAVE TECHNOLOGY, Vol. 6, No. 2, FEB.    1988, pp. 339-345-   Non-patent document 2: Y. Inoue et al., “Elimination of Polarization    Sensitivity in Silica-Based Wavelength Division Multiplexer Using a    Polyimide Half waveplate”, JOURNAL OF LIGHTWAVE TECHNOLOGY, Vol. 15,    No. 10, October 1997, pp. 1947-1957-   Non-patent document 3: B. L. Heffner, “Deterministic, Analytical    Complete Measurement of Polarization-Dependent Transmission Through    Optical Devices”, IEEE PHOTONICS TECHNOLOGY LETTERS, VOL. 4, NO. 5,    MAY 1992, pp. 451-454-   Non-patent document 4: M. Okuno et al., “Birefringence Control of    Silica Waveguides on Si and Its Application to a Polarization-Beam    Splitter/Switch”, JOURNAL OF LIGHTWAVE TECHNOLOGY, VOL. 12, NO. 4,    APRIL. 1994, pp. 625-633

DISCLOSURE OF THE INVENTION

A first aspect of the present invention is an optical signal processingdevice comprising a Mach-Zehnder interferometer circuit, theMach-Zehnder interferometer circuit comprising two couplers and two armwaveguides, each fabricated on a substrate, the two arm waveguidesconnecting the two couplers with each other, the Mach-Zehnderinterferometer circuit comprising a polarization rotation devicedisposed in a groove dividing each of the two arm waveguides into two,the polarization rotation device for converting horizontally polarizedlight into vertically polarized light and converting verticallypolarized light into horizontally polarized light, wherein a differencebetween values divided by an optical wavelength to be used is within arange of 2 m−0.2 to 2 m+0.2 (m is an integer including zero), the valuesbeing curvilinear integrals of the birefringence along the respectivetwo arm waveguides in an optical signal travelling direction.

A second aspect of the present invention is an optical processing devicecomprising a Mach-Zehnder interferometer circuit, the Mach-Zehnderinterferometer circuit comprising two couplers and two arm waveguides,each fabricated on a substrate, the two arm waveguides connecting thetwo couplers with each other, the Mach-Zehnder interferometer circuitcomprising two polarization rotation devices each disposed in a groovedividing each of the two arm waveguides into two, the polarizationrotation device for converting horizontally polarized light intovertically polarized light and converting vertically polarized lightinto horizontally polarized light, wherein phases of an optical signalconverted by one of the polarization rotation devices and an opticalsignal converted by the other one of the polarization rotation devicesare shifted from each other by n and a difference between birefringencevalues divided by an optical wavelength to be used is within a range of(2 m−1)−0.2 to (2 m−1)+0.2 (m is an integer including zero), thebirefringence values being curvilinear integrals of the birefringencealong the respective two arm waveguides in an optical signal travellingdirection.

In an embodiment of the present invention, the polarization rotationdevice of the optical signal processing device in the first aspect is ahalf-wave length plate disposed in such a manner that an opticalprincipal axis thereof is slanted at an angle of 45 degrees relative toa vertical line of the substrate plane and is also perpendicular to theoptical signal travelling direction.

In an embodiment of the present invention, the two polarization rotationdevices of the optical signal processing devices in the second aspectare half-wave length plates disposed in such a manner that each ofoptical principal axes thereof is slanted at an angle of 45 degreesrelative to a vertical line of the substrate plane and is alsoperpendicular to the light travelling direction, in which the opticalprincipal axis in one of the polarization rotation devices and theoptical principal axis in the other one of the polarization rotationdevices are perpendicular to each other.

In an embodiment of the present invention, the coupler of the opticalsignal processing device in the first and second aspects is adirectional coupler or a multimode interference-type coupler.

In an embodiment of the present invention, at least one of the two armwaveguides of the optical signal processing device in the first andsecond aspects has a width changing partially, whereby the birefringenceis adjusted such that the difference between the birefringence valuesbecomes a desired value, the birefringence values being curvilinearintegrals of the birefringence along the respective two arm waveguidesin the optical signal travelling direction.

In an embodiment of the present invention, at least one of the two armwaveguides of the optical signal processing device in the first andsecond aspects is partially irradiated with laser, thereby thebirefringence is adjusted such that the difference between thebirefringence values becomes a desired value, the birefringence valuesbeing curvilinear integrals of the birefringence along the respectivetwo arm waveguides in the optical signal travelling direction.

In an embodiment of the present invention, at least one of the two armwaveguides of the optical signal processing device in the first andsecond aspects has stress-releasing grooves formed partially at bothsides thereof, thereby the birefringence is adjusted such that thedifference between the birefringence values becomes a desired value, thebirefringence values being curvilinear integrals of the birefringencealong the respective two arm waveguides in the optical signal travellingdirection.

In an embodiment of the present invention, at least one of the two armwaveguides of the optical signal processing device in the first andsecond aspects has a stress-applying film formed over an upper surfacethereof, thereby the birefringence is adjusted such that the differencebetween the birefringence values becomes a desired value, thebirefringence values being curvilinear integrals along the respectivetwo arm waveguides in the optical signal travelling direction.

In an embodiment of the present invention, at least one of the two armwaveguides of the optical signal processing device in the first andsecond aspects has a thin film heater formed thereover for changingstress, thereby the birefringence is adjusted such that the differencebetween the birefringence values becomes a desired value, thebirefringence values being curvilinear integrals of the birefringencealong the respective two arm waveguides in the optical signal travellingdirection.

According to the present invention, it becomes possible to provide apolarization-independent waveguide-type optical interference circuitwhich suppresses the polarization dependence of the transmissionspectrum and the temperature dependence regarding the polarization.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a schematic diagram of a Mach-Zehnder interferometer circuitusing an optical waveguide;

FIG. 2 is a schematic diagram of a Mach-Zehnder interferometer circuitin a first example of a conventional technique;

FIG. 3 is a diagram for explaining a condition for a polarizationindependent transmission spectrum;

FIG. 4A is a diagram showing a calculation result of a PDf dependence ona birefringence when an operation wavelength of a half-wave length plateis shifted from a wavelength to be used by 4%;

FIG. 4B is an enlarged diagram of FIG. 4A;

FIG. 5A is a diagram in which the horizontal axis of FIG. 4A isexpressed by an order number;

FIG. 5B is an enlarged diagram of FIG. 5A;

FIG. 6 is a diagram for explaining a waveguide fabrication process of anoptical signal processing device in an embodiment of the presentinvention;

FIG. 7 is a schematic diagram of a Mach-Zehnder interferometer circuitfabricated as a first embodiment of the present invention;

FIG. 8 is a schematic diagram of a Mach-Zehnder interferometer circuitfabricated as a second embodiment of the present invention;

FIG. 9 is a schematic diagram of a Mach-Zehnder interferometer circuitfabricated as a third embodiment of the present invention;

FIG. 10 is a schematic diagram of a Mach-Zehnder interferometer circuitfabricated as a fourth embodiment of the present invention;

FIG. 11A is a schematic diagram of a Mach-Zehnder interferometer circuitfabricated as a fourth embodiment of the present invention;

FIG. 11B is a diagram for explaining a configuration of the half-wavelength plate in FIG. 11A; and

FIG. 11C is a diagram for explaining a configuration of the otherhalf-wave length plate in FIG. 11A.

BEST MODE FOR CARRYING OUT THE INVENTION

Hereinafter, embodiments of the present invention will be explained indetail with reference to the drawings.

First, with reference to FIG. 3, there will be explained apolarization-independent condition of a transmission spectrum even whenthe operation wavelength of the half-wave length plate is shifted fromthe design wavelength.

The problem is that the optical path length difference of the polarizedwaves which are not converted into the other polarization and theoptical path length difference of the polarized waves which areconverted into the other polarization do not coincide with each otherwhen the operation wavelength of the half-wave length plate is shiftedfrom the design wavelength. Accordingly, these optical path lengthdifferences are attempted to be made apparently the same.

Specifically, a difference between the optical path length differencen_(TE)ΔL of TE polarized waves which are input in the TE polarizationand travel without the polarization conversion, and the optical pathlength difference, given by the following formula, of the polarizedwaves which are input in the TM polarization and travel in the TEpolarization after the polarization conversion by the half-wave lengthplate is made to be zero or an integral multiple of the wavelength to beused.

$\begin{matrix}{\left( {n_{TE} + n_{TM}} \right) \cdot \frac{\Delta\; L}{2}} & \left\lbrack {{Formula}\mspace{14mu} 11} \right\rbrack\end{matrix}$

At the same time, a difference between the optical path lengthdifference n_(TM)ΔL of TM polarized waves which are input in the TMpolarization and travel without the polarization conversion, and theoptical path length difference, given by the following formula, of thepolarized waves which are input in the TE polarization and travels inthe TM polarization after the polarization conversion is made to be zeroor an integral multiple of the wavelength to be used.

$\begin{matrix}{\left( {n_{TE} + n_{TM}} \right) \cdot \frac{\Delta\; L}{2}} & \left\lbrack {{Formula}\mspace{14mu} 12} \right\rbrack\end{matrix}$

This will be explained more specifically by the use of formulas.

<Case of Principal Axes of the Half-Wave Length Plates Directed in theSame Direction/Through-Path>

An optical output which is the output of the wave after travellingthrough I1, the arm 1, and O1 is given by Formula (7) in the MZI, whichis the Mach-Zehnder interferometer having half-wave length platesinserted in the centers of two arm waveguides, respectively, in whichthe direction of the optical principal axis of each half-wave lengthplate is slanted at an angle of 45 degrees relative to a perpendicularline (vertical line) against the substrate plane and is perpendicular toa travelling direction of the optical signal, and the half-wave lengthplates inserted in the arm waveguides have the optical principal axes inthe same direction, respectively.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 13} \right\rbrack & \; \\{\frac{\sqrt{2}}{2}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\;\psi} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (7)\end{matrix}$

Here, φ_(TE) and φ_(TM) are phase differences between the two armwaveguides for the TE polarized wave and the TM polarized wave,respectively, Ψ is a phase difference provided by the half-wave lengthplate. Note that the coupling ratio of the coupler is assumed to be 50%and, from the assumption that the wave length plate has a shift from thedesign wavelength, Ψ is assumed to take a value except n and an integralmultiple thereof. Further, an optical output which is the output of thewave after travelling through I1, the arm 2, and O1 is given by Formula(8).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 14} \right\rbrack & \; \\{{- \frac{\sqrt{2}}{2}}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\;\psi} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (8)\end{matrix}$

By the use of Formulas (7) and (8), an optical output of thethrough-path is given by Formula (9).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 15} \right\rbrack & \; \\{\begin{pmatrix}O_{TE}^{th} \\O_{TM}^{th}\end{pmatrix} = {\frac{1}{4}\begin{pmatrix}\begin{matrix}{{{I_{TE}\left( {{\mathbb{e}}^{{- j}\;\phi_{TE}} - 1} \right)}\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right)} +} \\{{I_{TM}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} - 1} \right)}\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right)}\end{matrix} \\\begin{matrix}{{{I_{TE}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} - 1} \right)}\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right)} +} \\{{I_{TM}\left( {{\mathbb{e}}^{{- j}\;\phi_{TM}} - 1} \right)}\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right)}\end{matrix}\end{pmatrix}}} & (9)\end{matrix}$

In Formula (9), the polarization-independent condition at the extinctwavelength is obtained when the following formula is satisfied.

$\begin{matrix}{\begin{pmatrix}O_{TE}^{th} \\O_{TM}^{th}\end{pmatrix} = \begin{pmatrix}0 \\0\end{pmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 16} \right\rbrack\end{matrix}$

That is, the following formulas may be satisfied.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 17} \right\rbrack & \; \\{\phi_{TE} = {2\; m\;\pi}} & (10) \\{\phi_{TM} = {2\; n\;\pi}} & (11) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {2\;\alpha\;\pi}} & (12)\end{matrix}$

Here, m, n, and α each indicate integers and thus the following formulasare obtained.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 18} \right\rbrack & \; \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {{2\left( {\alpha - n} \right)\pi} = {2n^{\prime}\pi}}} & (13) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {2\;\alpha\;\pi}} & (14)\end{matrix}$

Formula (13) is converted into Formula (15).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 19} \right\rbrack & \; \\\begin{matrix}{{\phi_{TE} - \phi_{TM}} = {\begin{Bmatrix}{\left( {{\int{n_{TE}{\mathbb{d}l_{1}}}} - {\int{n_{TE}{\mathbb{d}l_{2}}}}} \right) -} \\\left( {{\int{n_{TM}{\mathbb{d}l_{1}}}} - {\int{n_{TM}{\mathbb{d}l_{2}}}}} \right)\end{Bmatrix}\frac{2\;\pi}{\lambda}}} \\{= {\left\{ {{\int{B{\mathbb{d}l_{1}}}} - {\int{B{\mathbb{d}l_{2}}}}} \right\}\frac{2\;\pi}{\lambda}}} \\{= {4\; n^{\prime}\pi}}\end{matrix} & (15)\end{matrix}$

By being rewritten further, Formula (16) is derived.[Formula 20]∫Bdl ₁ −∫Bdl ₂=2n′λ  (16)

From the above formula, the polarization independence is found to beobtained when the optical path length difference depending on thepolarization becomes an even number order of the extinction wavelength(wavelength to be used).

Generally, the birefringence value of the waveguide varies because ofthe fabrication error. However, a certain extent of variation is allowedfor satisfying the target condition such that the PDf is to be onehundredth of the FSR.

Accordingly, an acceptable value of the birefringence will be obtainedfor attaining the target PDf (or order number of the optical path lengthdifference depending on the polarization).

When the Jones matrix of the MZI is M, the maximum value and the minimumvalue of the optical output at a certain wavelength are derived byobtaining an eigenvalue for the product of the complex conjugatetransposed matrix of M (M*)^(T) and M (refer to Non-patent document 3).By the use of Formula (9), the Jones matrix of the MZI is expressed asfollows.

[Formula  21] $\begin{matrix}{M = {\frac{1}{4}\begin{pmatrix}{\left( {{\mathbb{e}}^{{- j}\;\phi_{TE}} - 1} \right)\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right)} & {\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} - 1} \right)\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right)} \\{\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} - 1} \right)\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right)} & {\left( {{\mathbb{e}}^{{- j}\;\phi_{TM}} - 1} \right)\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right)}\end{pmatrix}}} & (17)\end{matrix}$

The eigenvalue of (M*)^(T)M is calculated for a wavelength (orfrequency) and the PDf is derived by the calculation of a spectrumaround 1.55 μm.

FIGS. 4A and 4B show a calculation result of a relationship between thePDf and the birefringence when the operation wavelength of the half-wavelength plate is shifted from the wavelength to be used. The calculationassumes that the coupling ratio of the coupler is 50% and the operationwavelength of the half-wave length plate is shifted by 4% from thewavelength to be used. This is because the operating wavelength of thehalf-wave length plate used by the inventors has an error of 4%(standard deviation) from the design wavelength. FIGS. 4A and 4B showthat the variation of the birefringence may be ±0.1×10⁻⁴ or less formaking the PDf one hundredth of the FSR in the present invention.

FIGS. 5A and 5B show graphs in which each of the horizontal axes ofrespective FIGS. 4A and 4B is expressed by an order number (value of theoptical path length difference depending on the polarization Δ(BL)divided by the wavelength to be used). FIGS. 5A and 5B show that theacceptable variation of the order number is within a range of ±0.2order.

Similarly, the change of the PDf caused by the environmental temperaturechange can be analogized by the use of FIGS. 4A and 4B.

In FIGS. 4A and 4B, the bold line and the fine line indicate thebirefringence dependences of the PDf in the present invention and thesecond example of the conventional technique, respectively. Thebirefringence dependence of the PDf in the present invention is found tobe relaxed in comparison with the second example of the conventionaltechnique. That is, since the birefringence is changed by theenvironmental temperature, it is found that the environmentaltemperature dependence of the PDf is relaxed.

<Case of Principal Axes of the Half-Wave Length Plates Directed in theSame Direction/Cross Path>

Similarly for the cross pass, the condition of the polarizationindependence can be calculated at the extinction wavelength.

An optical output which is the output of the wave after travelingthrough I1, the arm 1, and O2 is given by Formula (18).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 22} \right\rbrack & \; \\{{- j}\frac{\sqrt{2}}{2}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\;\psi} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (18)\end{matrix}$

Here, φ_(TE) and φ_(TM) are phase differences between the two armwaveguides for the TE polarized wave and the TM polarized wave,respectively, and Ψ is a phase difference provided by the half-wavelength plate. The coupling ratio of the coupler is assumed to be 50%.Further, an optical output which is the output of the wave aftertravelling through I1, the arm 2, and O2 is given by Formula (19).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 23} \right\rbrack & \; \\{{- j}\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\;\psi} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (19)\end{matrix}$

By the use of the above two formulas, the optical output for the crosspath is expressed by Formula (20).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 24} \right\rbrack & \; \\{\begin{pmatrix}O_{TE}^{\alpha} \\O_{TM}^{\alpha}\end{pmatrix} = {{- j}\frac{1}{4}\begin{pmatrix}\begin{matrix}{{\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right){I_{TE}\left( {{\mathbb{e}}^{{- j}\;\phi_{TE}} + 1} \right)}} +} \\{\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right){I_{TM}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}}\end{matrix} \\\begin{matrix}{{\left( {{\mathbb{e}}^{{- j}\;\psi} - 1} \right){I_{TE}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}} +} \\{\left( {{\mathbb{e}}^{{- j}\;\psi} + 1} \right){I_{TM}\left( {{\mathbb{e}}^{{- j}\;\phi_{TM}} + 1} \right)}}\end{matrix}\end{pmatrix}}} & (20)\end{matrix}$

In Formula (20), the polarization-independent condition at theextinction wavelength is obtained when the following formula issatisfied.

$\begin{matrix}{\begin{pmatrix}O_{TE}^{th} \\O_{TM}^{th}\end{pmatrix} = \begin{pmatrix}0 \\0\end{pmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 25} \right\rbrack\end{matrix}$

That is, the following formulas may be satisfied.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 26} \right\rbrack & \; \\{\phi_{TE} = {\left( {{2\; m} + 1} \right)\pi}} & (21) \\{\phi_{TM} = {\left( {{2\; n} + 1} \right)\pi}} & (22) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\left( {{2\;\alpha} + 1} \right)\pi}} & (23)\end{matrix}$

Here, m, n, and α each indicate integers and the following formulas areobtained.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 27} \right\rbrack & \; \\{\frac{\phi_{TE} - \phi_{TM}}{2} = {{2\left( {\alpha - n} \right)\pi} = {2n^{\prime}\pi}}} & (24) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\left( {{2\alpha} + 1} \right)\pi}} & (25)\end{matrix}$

By being rewritten further, Formula (26) is derived.[Formula 28]∫Bdl ₁ −∫Bdl ₂=2n′λ  (26)

The above formula shows that the polarization independence is obtainedwhen the optical path length difference depending on the polarizationbecomes an even number order at a certain extinction wavelength.

<Case of Principal Axes of the Half-Wave Length Plates beingPerpendicular to Each Other/Through-Path>

An optical output which is the output of the wave after travellingthrough I1, the arm 1, and O1 is given by Formula (27) in the MZI, whichis the Mach-Zehnder interferometer having half-wave length platesinserted in the centers of two arm waveguides, respectively, in whichthe optical principal axis direction of each of the half-wave lengthplates is slanted at an angle of 45 degrees relative to a line (verticalline) perpendicular to the substrate plane and is perpendicular to atravelling direction of the optical signal, and the half-wave lengthplates inserted in the respective arm waveguides have the opticalprincipal axes perpendicular to each other.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 29} \right\rbrack & \; \\{\frac{\sqrt{2}}{2}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{- {j\psi}} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (27)\end{matrix}$

Further, an optical output which is the output of the wave aftertravelling through I1, the arm 2, and O1 is given by Formula (28).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 30} \right\rbrack & \; \\{{- \frac{\sqrt{2}}{2}}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{- {j\psi}} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (28)\end{matrix}$

By the use of Formulas (27) and (28), an optical output of thethrough-path is given by Formula (29).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 31} \right\rbrack & \; \\{\begin{pmatrix}O_{TE}^{th} \\O_{TM}^{th}\end{pmatrix} = {\frac{1}{4}\begin{pmatrix}{{\left( {{\mathbb{e}}^{- {j\psi}} + 1} \right){I_{TE}\left( {{\mathbb{e}}^{- {j\phi}_{TE}} - 1} \right)}} + {\left( {{\mathbb{e}}^{- {j\psi}} - 1} \right){I_{TM}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}}} \\{{\left( {{\mathbb{e}}^{- {j\psi}} - 1} \right){I_{TE}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}} + {\left( {{\mathbb{e}}^{- {j\psi}} + 1} \right){I_{TM}\left( {{\mathbb{e}}^{- {j\phi}_{TM}} - 1} \right)}}}\end{pmatrix}}} & (29)\end{matrix}$

In Formula (29), the polarization-independent condition at theextinction wavelength is obtained when the following formula issatisfied.

$\begin{matrix}{\begin{pmatrix}O_{TE}^{th} \\O_{TM}^{th}\end{pmatrix} = \begin{pmatrix}0 \\0\end{pmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 32} \right\rbrack\end{matrix}$

That is, the following formulas may be satisfied.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 33} \right\rbrack & \; \\{\phi_{TE} = {2m\;\pi}} & (30) \\{\phi_{TM} = {2n\;\pi}} & (31) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\pi\left( {{2\alpha} + 1} \right)}} & (32)\end{matrix}$

Here, m, n, and α each indicate integers and thus the following formulasare obtained.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 34} \right\rbrack & \; \\{\frac{\phi_{TE} - \phi_{TM}}{2} = {{\left\{ {{2\left( {\alpha - n} \right)} + 1} \right\}\pi} = {\left( {{2n^{\prime}} + 1} \right)\pi}}} & (33) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\pi\left( {{2\alpha} + 1} \right)}} & (34)\end{matrix}$

By being rewritten further, Formula (35) is derived.[Formula 35]∫Bdl ₁ −∫Bdl ₂=(2n′+1)λ  (35)

This formula shows that the polarization independence is obtained whenthe optical path length difference depending on the polarization becomesan odd number order at a certain extinction wavelength.

<Case of Principal Axes of the Half-Wave Length Plates BeingPerpendicular to Each Other/Cross Path>

For the cross pass, a condition of the polarization independence can becalculated similarly.

An optical output which is the output of the wave after travelingthrough I1, the arm 1, and O2 is given by Formula (36).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 36} \right\rbrack & \; \\{{- j}\frac{\sqrt{2}}{2}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{- {j\psi}} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{{- j}\frac{\phi_{TE}}{2}} & 0 \\0 & {\mathbb{e}}^{{- j}\frac{\phi_{TM}}{2}}\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (36)\end{matrix}$

Here, φ_(TE) and φ_(TM) are phase differences between the two armwaveguides for the TE polarized wave and the TM polarized wave,respectively, and Ψ is a phase difference provided by the half-wavelength plate. The coupling ratio of the coupler is assumed to be 50%.Further, an optical output which is the output of the wave aftertravelling through I1, arm 2, and O2 is given by Formula (37).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 37} \right\rbrack & \; \\{{- j}\frac{\sqrt{2}}{2}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & 1 \\{- 1} & 1\end{pmatrix}\begin{pmatrix}{\mathbb{e}}^{- {j\psi}} & 0 \\0 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}1 & {- 1} \\1 & 1\end{pmatrix}\frac{\sqrt{2}}{2}\begin{pmatrix}I_{TE} \\I_{TM}\end{pmatrix}} & (37)\end{matrix}$

By the use of the above two formulas, the optical output for the thrcross path is expressed by Formula (38).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 38} \right\rbrack & \; \\{\begin{pmatrix}O_{TE}^{cr} \\O_{TM}^{cr}\end{pmatrix} = {{- j}\frac{1}{4}\begin{pmatrix}{{{I_{TE}\left( {{\mathbb{e}}^{- {j\phi}_{TE}} - 1} \right)}\left( {{\mathbb{e}}^{- {j\psi}} + 1} \right)} + {{I_{TM}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}\left( {{\mathbb{e}}^{- {j\psi}} - 1} \right)}} \\{{{I_{TE}\left( {{\mathbb{e}}^{{- j}\frac{\phi_{TE} + \phi_{TM}}{2}} + 1} \right)}\left( {{\mathbb{e}}^{- {j\psi}} - 1} \right)} + {{I_{TM}\left( {{\mathbb{e}}^{- {j\phi}_{TM}} - 1} \right)}\left( {{\mathbb{e}}^{- {j\psi}} + 1} \right)}}\end{pmatrix}}} & (38)\end{matrix}$

In Formula (38), the polarization-independent condition at theextinction wavelength is obtained when the following formula issatisfied.

$\begin{matrix}{\begin{pmatrix}O_{TE}^{cr} \\O_{TM}^{cr}\end{pmatrix} = \begin{pmatrix}0 \\0\end{pmatrix}} & \left\lbrack {{Formula}\mspace{14mu} 39} \right\rbrack\end{matrix}$

That is, the following formulas may be satisfied.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 40} \right\rbrack & \; \\{\phi_{TE} = {2m\;\pi}} & (39) \\{\phi_{TM} = {2n\;\pi}} & (40) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\pi\left( {{2\alpha} + 1} \right)}} & (41)\end{matrix}$

Accordingly, the following formulas are obtained.

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 41} \right\rbrack & \; \\{\frac{\phi_{TE} - \phi_{TM}}{2} = {{\left\{ {{2\left( {\alpha - n} \right)} + 1} \right\}\pi} = {\left( {{2n^{\prime}} + 1} \right)\pi}}} & (42) \\{\frac{\phi_{TE} + \phi_{TM}}{2} = {\pi\left( {{2\alpha} + 1} \right)}} & (43)\end{matrix}$

By being rewritten further, Formula (44) is derived.[Formula 42]∫Bdl ₁ −∫Bdl ₂=(2n′+1)λ  (44)

The above formula shows that the polarization independence is obtainedwhen the optical path length difference depending on the polarizationbecomes an odd number order at a certain extinction wavelength.

In the following, embodiments of the present invention will be explainedin detail with reference to the drawings.

Note that the explanation in the following will be provided by taking asan example a silica optical waveguide formed on a silicon substrate forthe optical waveguide. This is because this combination is suitable forthe fabrication of the optical waveguide which is stable and has adistinguished reliability. However, the present invention is not limitedto this combination and it is needless to say that the combination maybe a silica optical waveguide, an optical waveguide such as asilicon-oxide/nitride (SiON) film, an organic optical waveguide such asPMMA (Polymethylmethacrylate) resin, or a silicon optical waveguide on asubstrate such as silicon, silica glass, or soda glass.

Further, the explanation in the following will be provided by taking asan example a multimode interferometer-type coupler for the coupler, butalso a directional coupler can be used.

A fabrication process of the waveguide of the present invention will bebriefly explained with reference to FIG. 6. Underclad glass fineparticles 604 mainly made of SiO₂ and core glass fine particles 606 madeof SiO₂ doped with GeO₂ are sequentially deposited on a siliconsubstrate 602 by a flame hydrolysis deposition method (FHD) (FIG. 6(1)).In this stage, the glass particles look white because of lightscattering by the glass particles.

After that, the glass is made transparent at a high temperature above1000° C. When the silicon substrate having the glass particles depositedon the surface thereof is heated gradually, the glass particles aremelted and a transparent glass film is formed. At this time, the glassfine particles are deposited in such a manner that the thickness of theunderclad glass layer 604 becomes 30 microns and the thickness of thecore glass layer 606 becomes 7 microns (FIG. 6(2)).

Subsequently, the core glass layer 606 is patterned by aphotolithography technique and reactive ion etching (RIE) (FIG. 6(3)).

Overclad glass fine particles 608 are deposited over the core by theflame hydrolysis deposition method (FIG. 6(4). Last, thehigh-temperature transparency processing is carried out to fabricate anembedded waveguide (FIG. 6(5)). The glass transition temperature of theoverclad glass layer 608 is reduced by the addition of boron trioxideand phosphorus pentoxide as dopant so as not to deform the core in thelast high-temperature transparency processing.

Embodiment 1

FIG. 7 shows a schematic diagram of an MZI fabricated as a firstembodiment of the present invention. The MZI 700 shown in FIG. 7 isprovided with two multimode interferometer-type couplers (722, 724) andtwo arm waveguides (706, 708) connecting the two multimodeinterferometer-type couplers with each other. Further, the MZI 700 isprovided with a half-wave length plate 732 inserted in a groove formedso as to divide the arm waveguide 706 at the center thereof into an armwaveguide 706 a and a arm waveguide 706 b for dividing the optical pathlength of the arm waveguide 706 into two, and so as to divide the armwaveguide 708 at the center thereof into an arm waveguide 708 a and anarm waveguide 708 b for dividing the optical path length of the armwaveguide 708 into two. The multimode interferometer-type coupler 722 isprovided with two input waveguides (702, 704) and the multimodeinterferometer-type coupler 724 is provided with two output waveguides(710, 712).

The half-wave length plate 732 as a polarization rotation device is apolyimide wave length plate, and the optical principal axis thereof isperpendicular to a traveling direction and also is slanted at an angleof 45 degrees relative to the horizontal direction of the substrateplane (or vertical line of the substrate plane). The half-wave lengthplate 732 provides the polarized waves traveling along a slow axis and afast axis thereof with a phase shift corresponding to a half wavelengthof the design wavelength, respectively, and has the function ofconverting the TM polarization into the TE polarization and convertingthe TE polarization into the TM polarization.

In this MZI 700, the path difference (ΔL) between the two arm waveguides(706, 708) is set to be 20.7 mm for setting the FSR 10 GHz.

Further, in the MZI of the present embodiment, the birefringence isadjusted by irradiating a part of the arm waveguide around the half-wavelength plate 732 with an ArF (argon fluoride) laser. Thus, thepolarization dependence is suppressed by setting Δ(BL) zero in this MZI700.

A method for setting Δ(BL) zero will be explained specifically in thefollowing.

In the arm waveguide 1 (706), the waveguide length in the laserirradiation region is denoted by L^(ir) ₁ and the waveguide length inthe laser non-irradiation region is denoted by L^(non) ₁. In the armwaveguide 2 (708), the waveguide length in the laser irradiation regionis denoted by L^(ir) ₂ and the waveguide length in the lasernon-irradiation region is denoted by L^(non) ₂. The birefringence in thelaser irradiation region is denoted by B^(ir) and the birefringence inthe laser non-irradiation region is denoted by B^(non). By the use ofthese symbols, Δ(BL) is expressed by Formula (45).[Formula 43]Δ(BL)=(L ₁ ^(ir) B ^(ir) +L ₁ ^(non) B ^(non))−(L ₂ ^(ir) B ^(ir) +L ₂^(non) B ^(non))  (45)

By the assumption of L^(ir) ₁=0 for simplicity, Formula (46) isobtained.[Formula 44]Δ(BL)=L ₁ ^(non) B ^(non)−(L ₁ ^(ir) B ^(ir) +L ₂ ^(non) B ^(non))=ΔLB^(non) −L ₂ ^(ir) ΔB  (46)

Here, the path difference between the two arm waveguides is given in thefollowing formula.ΔL=L ₁ ^(non)−(L ₂ ^(non) +L ₂ ^(ir))  [Formula 45]

Further, the birefringence difference is expressed by ΔB=B^(ir)−B^(non).The condition of setting Formula (46) zero is given by Formula (47).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 46} \right\rbrack & \; \\{L_{2}^{ir} = \frac{\Delta\;{LB}^{non}}{\Delta\; B}} & (47)\end{matrix}$

Accordingly, L^(ir) ₂ was set to be 10 mm so as to satisfy Formula (47)and the laser irradiation was carried out so as to make ΔB 2.1×10⁻⁴. AnArF excimer laser having a wavelength of 193 nm was used for the lasersource, and irradiation power, a pulse repetition rate, and irradiationtime were set to be 1 J/cm², 50 Hz, and 530 sec, respectively. Further,the laser irradiation was carried out by the use of a metal mask only inthe two laser irradiation regions being not covered by the metal maskand putting the half-wave length plate between thereof. An irradiationarea was 50 μm×50 mm. Meanwhile, ΔL was 20.7 mm and B^(non) was 1×10⁻⁴,and Δ(BL) became nearly zero.

According to the present embodiment, the PDf was able to be suppresseddown to 0.04 GHz for both of the cross path and the through-path arounda wavelength of 1.55 μm. The PDf in the first conventional technique was0.35 GHz for both of the cross path and the through-path. Accordingly,the PDf was able to be suppressed by the use of the present invention.

Further, when the environmental temperature was changed from −10° C. to80° C., the variation of the PDf was 0.06 GHz for both of the cross pathand the through-path. Meanwhile, in the MZI of the second conventionaltechnique, this variation of the PDf was 6 GHz for both of the crosspath and the through-path. Accordingly, the temperature dependence ofthe PDf was able to be reduced by the use of the present invention.

Note that the parts of the arm waveguides (706, 708) to be irradiatedwith the ArF laser may be apart from the half-wave length plate 732 anddo not need to be symmetrical with respect to the half-wave length plateif the irradiation amounts are symmetrical.

The ArF excimer laser having a wavelength of 193 nm was used foradjusting the birefringence in the present embodiment. This is becausethe refractive index change of the core is caused by absorption relatedto GeO₂ at a wavelength of 245 nm and the efficient refractive indexchange or birefringence change become possible by the irradiation of alaser having an oscillation wavelength around 245 nm. Further, evenvisible laser can induce a similar change by two photon absorption.Accordingly, the laser is not limited to the ArF excimer laser and it ispossible to use various kinds of excimer laser such as He—Cd laser, N₂laser, KrF excimer laser, and F₂ excimer laser, and laser having awavelength in an ultraviolet or visible range such as the second, third,and fourth harmonics of Ar ion laser, Nd³⁺:YAG laser, and alexandrite(Cr³⁺:BeAl₂O₃) laser.

Although the ArF laser was used as a birefringence adjustment method inthe present embodiment, a similar effect can be obtained by the use ofthe following birefringence adjustment methods, for example.

(1) It is possible to use a method in which a stress-applying film isdisposed over the waveguide to change stress induced in the waveguidefor controlling the birefringence (refer to Non-patent document 4). Thatis, the stress-applying film (not shown in the drawing) is formed overthe arm waveguide (706, 708) and the stress induced in the waveguide canbe adjusted in such a manner that a difference between values in whichbirefringence values are integrated along the two arm waveguides in thetravelling direction of the optical signal, respectively, becomes adesired value.

(2) It is possible to use a method in which a thin film heater above thewaveguide is partially heated to control the effective refraction indexor the birefringence permanently (refer to Patent document 2). That is,the thin film heater (not shown in the drawing) are formed above thewaveguide (706, 708) and the stress induced in the waveguide can beadjusted by the control such that a difference between values in whichbirefringence values are integrated along the two arm waveguides in thetravelling direction of the optical signal, respectively, become adesired value.

(3) It is possible to use a method in which a stress-releasing groovesare provided on both sides of the waveguide to release the stressapplied to the waveguide and to control the effective refractive indexor the birefringence (refer to Patent document 1). That is, thestress-releasing grooves (not shown in the drawing) are formed at a partof the arm waveguide on both sides in such a manner that a differencebetween values obtained by lineally integrating the birefringence forthe two arm waveguides (706, 708) in the traveling direction of theoptical signal, becomes a desired value, and the birefringence can beadjusted.

Embodiment 2

FIG. 8 shows a schematic diagram of an MZI fabricated as a secondembodiment of the present invention. The MZI 800 shown in FIG. 8 isprovided with two multimode interferometer-type couplers (822, 824) andtwo arm waveguides (806, 808) connecting the two multimodeinterferometer-type couplers with each other. Further, the MZI 800 isprovided with a half-wave length plate 832 inserted in a groove formedso as to divide the arm waveguide 806 at the center thereof into an armwaveguide 806 a and a arm waveguide 806 b for dividing the optical pathlength of the arm waveguide 806 into two, and so as to divide the armwaveguide 808 at the center thereof into an arm waveguide 808 a and anarm waveguide 808 b for dividing the optical path length of the armwaveguide 808 into two. The multimode interferometer-type coupler 822 isprovided with two input waveguides (802, 804) and the multimodeinterferometer-type coupler 824 is provided with two output waveguides(810, 812).

The configuration, arrangement, and function of the half-wave lengthplate 832 as the polarization rotation device are the same as those ofthe half-wave length plate 732 in the first embodiment.

The MZI 800 of the present embodiment carries out the birefringenceadjustment by changing the widths of the two arm waveguides (806, 808).It becomes possible to set the optical path length difference dependingon the polarization Δ(BL) to be zero by the change of the waveguidewidths (refer to Patent document 3).

The widths of the arm waveguides (806, 808) are set to be 7 μm near themultimode interferometer-type couplers (822, 824) and the arm waveguidewidths are set to be 12 μm near the half-wave length plate 832.

In this MZI 800, the path difference (ΔL) between the two arm waveguides(806, 808) is set to be 20.7 mm in the same way as that between the twoarm waveguides (706, 708) in the first embodiment.

An effect of using the two waveguide widths will be explainedspecifically by the use of formulas. For the arm waveguide 1, the lengthof the wide waveguide is denoted by L^(w) ₁ and the length of the narrowwaveguide is denoted by L^(n) ₁. For the arm waveguide 2, the length ofthe wide waveguide is denoted by L^(w) ₂ and the length of the narrowwaveguide is denoted by L^(n) ₂. Further, the birefringence of the widewaveguide is denoted by B^(w) and the birefringence of the narrowwaveguide is denoted by B^(n). By the use of these symbols, a differencebetween integrated birefringence values of the two arm waveguides in thetravelling direction is given by Formula (48).[Formula 47]Δ(BL)=(L ₁ ^(w) B ^(w) +L ₁ ^(n) B ^(n))−(L ₂ ^(w) B ^(w) +L ₂ ^(n) B^(n))  (48)

By the assumption of L^(w) ₁=0 for simplicity, Formula (49) is obtained.[Formula 48]Δ(BL)=L ₁ ^(n) B ^(n)−(L ₂ ^(w) B ^(w) +L ₂ ^(n) B ^(n))=ΔLB ^(n) −L ₂^(w) ΔB  (49)

Here, the length difference between the two arm waveguides is given bythe following formula and a difference in the birefringence is given asΔB=B^(w)−B^(n).ΔL=L ₁ ^(n)−(L ₂ ^(w) +L ₂ ^(n))  [Formula 49]

The condition of making Formula (49) zero is given by

-   -   Formula (50).

$\begin{matrix}\left\lbrack {{Formula}\mspace{14mu} 50} \right\rbrack & \; \\{L_{2}^{w} = \frac{\Delta\;{LB}^{n}}{\Delta\; B}} & (50)\end{matrix}$

L^(w) ₂ was determined in consideration of satisfying the above formula.Specific values were set as follows; B^(w)=1.57×10−4, B^(n)=0.8×10−4,L^(w) ₁=0.5 mm, and L^(w) ₂=26.2 mm.

Here, the wide waveguide is not necessary for the arm waveguide 1 onlyfor making Δ(BL) zero, but the wide waveguide is preferably disposedalso for the arm waveguide 1 from the following reasons.

-   -   A loss difference in the case of the presence or absence of the        taper waveguide is eliminated between the arm waveguides.    -   A diffraction loss of radiation in a half-wave length plate        without a confining structure is suppressed when the width of        the waveguide divided by the half-wave length plate is made        wider.

According to the present embodiment, the PDf was able to be suppresseddown to 0.05 GHz at a wavelength around 1.55 μm for both of the crosspath and the through-path.

Further, when the environmental temperature was changed from −10° C. to80° C., the PDf variation was able to be suppressed down to 0.06 GHz forboth of the cross path and the through-path.

Embodiment 3

FIG. 9 shows a schematic diagram of an MZI fabricated as a thirdembodiment of the present invention. The MZI 900 shown in FIG. 9 isprovided with two multimode interferometer-type couplers (922, 924) andtwo arm waveguides (906, 908) connecting the two multimodeinterferometer-type couplers with each other. Further, the MZI 900 isprovided with a half-wave length plate 932 inserted in a groove formedso as to divide the arm waveguide 906 at the center thereof into an armwaveguide 906 a and an arm waveguide 906 b for dividing the optical pathlength of the arm waveguide 906 into two, and so as to divide the armwaveguide 908 at the center thereof into an arm waveguide 908 a and anarm waveguide 908 b for dividing the optical path length of the armwaveguide 908 into two. The multimode interferometer-type coupler 922 isprovided with two input waveguides (902, 904) and the multimodeinterferometer-type coupler 924 is provided with two output waveguides(910, 912).

The configuration, arrangement, and function of the half-wave lengthplate 932 as the polarization rotation device are the same as those ofthe half-wave length plate 732 in the first embodiment.

In this MZI 900, a path difference (ΔL) between the two arm waveguides(906, 908) is set to be 20.7 mm the same as that between the two armwaveguides (706, 708) in the first embodiment.

A feature of this configuration is that the birefringence value is setto be 1.5×10⁻⁴. Here, the birefringence was adjusted by the change ofthe thermal expansion coefficient and the softening temperature in theoverclad glass. That is, the overclad glass was doped with borontrioxide at a rate of 10 mol % and phosphorus pentoxide at a rate of 10mol % relative to silica. As a result, the optical path differencedepending on the polarization Δ(BL) becomes 3.1×10⁻⁴ from the followingformula.[Formula 51]Δ(BL)=∫Bdl ₁ −∫Bdl ₂=1.5×10⁻⁴×20.7×10⁻³=3.1×10⁻⁶  (51)

This optical path length difference depending on the polarization Δ(BL)has an order number of 2 when the wavelength to be used is 1.55 μm andnearly satisfies Formula (16) and also Formula (26).

According to the present embodiment, the PDf was able to be suppresseddown to 0.006 GHz at a wavelength around 1.55 μm for both of the crosspath and the through-path.

Further, when the environmental temperature was changed from −10° C. to80° C., the PDf variation was able to be suppressed down to 0.06 GHz forboth of the cross path and the through-path.

Embodiment 4

FIGS. 10 and 11 show schematic diagrams of an MZI fabricated as a fourthembodiment of the present invention. The MZI 1000 is provided with twomultimode interferometer-type couplers (1022, 1024) and two armwaveguides (1006, 1008) connecting the two multimode interferometer-typecouplers with each other, each fabricated on a silicon substrate 1102.Further, the MZI 1000 is provided with a half-wave length plate 1032inserted in a groove 1120 formed so as to divide the arm waveguide 1006at the center thereof into an arm waveguide 1006 a and a arm waveguide1006 b for dividing the optical path length of the arm waveguide 1006into two, and so as to divide the arm waveguide 1008 at the centerthereof into an arm waveguide 1008 a and an arm waveguide 1008 b fordividing the optical path length of the arm waveguide 1008 into two. Themultimode interferometer-type coupler 1022 is provided with two inputwaveguides (1002, 1004) and the multimode interferometer-type coupler1024 is provided with two output waveguides (1010, 1012).

As shown in FIG. 11A, the half-wave length plate 1032 as thepolarization rotation device includes a half-wave length plate 1032 aand a half-wave length plate 1032 b. Each of the half-wave length plate1032 a and the half-wave length plate 1032 b, as shown in FIGS. 11B and11C, respectively, has an optical principal axis which is perpendicularto the travelling direction and also is slanted at an angle of 45degrees relative to the horizontal direction (or vertical direction) ofthe substrate, and the principal axis direction of the half-wave lengthplate 1032 a and the principal axis direction of the half-wave lengthplate 1032 b are perpendicular to each other.

Each of the half-wave length plate 1032 a and the half-wave length plate1032 b provides the polarized waves traveling along a slow axis and afast axis thereof, respectively with a phase shift corresponding to ahalf wavelength of the design wavelength. The half-wave length plate1032 has the function of converting the TM polarization into the TEpolarization and converting the TE polarization into the TMpolarization.

In the present embodiment, the overclad glass was doped with borontrioxide at a rate of 20 mol % and phosphorus pentoxide at a rate of 5mol % relative to silica, and the birefringence value was set to be0.775×10⁻⁴. As a result, the optical path difference depending on thepolarization becomes 1.55×10⁻⁶ from Formula (52).[Formula 52]∫Bdl ₁ −Bdl ₂=Δ(BL)=0.775×10⁻⁴×20.7×10⁻³=1.55×10⁻⁶  (52)

This optical path length difference depending on the polarization Δ(BL)has an order number of 1 when the wavelength to be used is 1.55 μm andcan nearly satisfies Formula (35) and also Formula (44).

According to the present embodiment, the PDf was able to be suppresseddown to 0.07 GHz at a wavelength around 1.55 μm for both of the crosspath and the through-path.

Further, when the environmental temperature was changed from −10° C. to80° C., the PDf variation was able to be suppressed down to 0.06 GHz forboth of the cross path and the through-path.

It is needless to say that the birefringence value can be adjusted bythe application of the above first to third embodiments to the presentembodiment.

Further, the above embodiments used the MZI having a FSR of 10 GHz. Itis obvious that the same effect can be expected even for another FSRvalue such as 20 GHz or 40 GHz in addition to the above FSR value.

1. An optical signal processing device comprising a Mach-Zehnderinterferometer circuit, the Mach-Zehnder interferometer circuitcomprising two couplers and two arm waveguides, each fabricated on asubstrate, the two arm waveguides connecting the two couplers with eachother, the Mach-Zehnder interferometer circuit comprising: apolarization rotation device disposed in a groove dividing each of thetwo arm waveguides into two, the polarization rotation device forconverting horizontally polarized light into vertically polarized lightand converting vertically polarized light into horizontally polarizedlight, wherein a difference between birefringence values divided by anoptical wavelength to be used is within a range of 2 m-0.2 to 2 m+0.2 (mis an integer including zero), the birefringence values beingcurvilinear integrals of the birefringence along the respective two armwaveguides in an optical signal travelling direction.
 2. The opticalsignal processing device according to claim 1, wherein the polarizationrotation device is a half-wave length plate disposed in such a mannerthat an optical principal axis thereof is slanted at an angle of 45degrees relative to a vertical line of the substrate plane and is alsoperpendicular to the optical signal travelling direction.
 3. The opticalsignal processing device according to claim 1, wherein the coupler is adirectional coupler or a multimode interference-type coupler.
 4. Theoptical signal processing device according to claim 1, wherein at leastone of the two arm waveguides has a width changing partially, therebythe birefringence is adjusted such that the difference between thebirefringence values becomes a desired value, the birefringence valuesbeing curvilinear integrals of the birefringence along the respectivetwo arm waveguides in the optical signal travelling direction.
 5. Theoptical signal processing device according to claim 1, wherein at leastone of the two arm waveguides is partially irradiated with laser,thereby the birefringence is adjusted such that the difference betweenthe birefringence values becomes a desired value, the birefringencevalues being curvilinear integrals of the birefringence along therespective two arm waveguides in the optical signal travellingdirection.
 6. The optical signal processing device according to claim 1,wherein at least one of the two arm waveguides has stress-releasinggrooves formed partially at both sides thereof, thereby thebirefringence is adjusted such that the difference between thebirefringence values becomes a desired value, the birefringence valuesbeing curvilinear integrals of the birefringence along the respectivetwo arm waveguides in the optical signal travelling direction.
 7. Theoptical signal processing device according to claim 1, wherein at leastone of the two arm waveguides has a stress-applying film formed over anupper surface thereof, thereby the birefringence is adjusted such thatthe difference between the birefringence values becomes a desired value,the birefringence values being curvilinear integrals along therespective two arm waveguides in the optical signal travellingdirection.
 8. The optical signal processing device according to claim 1,wherein at least one of the two arm waveguides has a thin film heaterformed thereover for changing stress, thereby the birefringence isadjusted such that the difference between the birefringence valuesbecomes a desired value, the birefringence values being curvilinearintegrals of the birefringence along the respective two arm waveguidesin the optical signal travelling direction.
 9. An optical signalprocessing device comprising a Mach-Zehnder interferometer circuit, theMach-Zehnder interferometer circuit comprising two couplers and two armwaveguides, each fabricated on a substrate, the two arm waveguidesconnecting the two couplers with each other, the Mach-Zehnderinterferometer circuit comprising: two polarization rotation deviceseach disposed in a groove dividing each of the two arm waveguides intotwo, the polarization rotation device for converting horizontallypolarized light into vertically polarized light and convertingvertically polarized light into horizontally polarized light, andwherein a difference between birefringence values divided by an opticalwavelength to be used is within a range of (2 m−1)-0.2 to (2 m−1)+0.2 (mis an integer including zero), the birefringence values beingcurvilinear integrals of the birefringence along the respective two armwaveguides in an optical signal travelling direction.
 10. The opticalsignal processing device according to claim 9, wherein the twopolarization rotation devices are half-wave length plates disposed insuch a manner that each of optical principal axes thereof is slanted atan angle of 45 degrees relative to a vertical line of the substrateplane and is also perpendicular to the optical signal travellingdirection, in which the optical principal axis in one of thepolarization rotation devices and the optical principal axis in theother one of the polarization rotation devices are perpendicular to eachother.
 11. The optical signal processing device according to claim 9,wherein the coupler is a directional coupler or a multimodeinterference-type coupler.
 12. The optical signal processing deviceaccording to claim 9, wherein at least one of the two arm waveguides hasa width changing partially, thereby the birefringence is adjusted suchthat the difference between the birefringence values becomes a desiredvalue, the birefringence values being curvilinear integrals of thebirefringence along the respective two arm waveguides in the opticalsignal travelling direction.
 13. The optical signal processing deviceaccording to claim 9, wherein at least one of the two arm waveguides ispartially irradiated with laser, thereby the birefringence is adjustedsuch that the difference between the birefringence values becomes adesired value, the birefringence values being curvilinear integrals ofthe birefringence along the respective two arm waveguides in the opticalsignal travelling direction.
 14. The optical signal processing deviceaccording to claim 9, wherein at least one of the two arm waveguides hasstress-releasing grooves formed partially at both sides thereof, therebythe birefringence is adjusted such that the difference between thebirefringence values becomes a desired value, the birefringence valuesbeing curvilinear integrals of the birefringence along the respectivetwo arm waveguides in the optical signal travelling direction.
 15. Theoptical signal processing device according to claim 9, wherein at leastone of the two arm waveguides has a stress-applying film formed over anupper surface thereof, thereby the birefringence is adjusted such thatthe difference between the birefringence values becomes a desired value,the birefringence values being curvilinear integrals along therespective two arm waveguides in the optical signal travellingdirection.
 16. The optical signal processing device according to claim9, wherein at least one of the two arm waveguides has a thin film heaterformed thereover for changing stress, thereby the birefringence isadjusted such that the difference between the birefringence valuesbecomes a desired value, the birefringence values being curvilinearintegrals of the birefringence along the respective two arm waveguidesin the optical signal travelling direction.